ON THE PRINCIPLE OF RELATIVITY. 245 



9. 



It becomes, therefore, a question of great interest to ask whether 

 experiment can say anything about gravitation in the light of the theory 

 of relativity. Poincare G has shown how to obtain modified laws conforming 

 to the principle of relativity, and de Sitter 7 has examined two of these 

 in the light of the effect they would have on the planetary orbits. 



The equations proposed in place of the ordinary equation 



d?x kx 



^ + £=0 .... (I.) 



-* ss + £-° < tt > 



where r is a new variable connected with t by the relation 



dr , 



v being the velocity of the planet relative to the sun at time t. 



The analysis shows that neither of these leads to any observable 

 periodic or secular change in the orbits, except in the case of Mercury, 

 where it would give rise to a motion of the apse line which would be within 

 the reach of modern measurements were it not concealed in a larger 

 motion of the same kind attributed to a different cause. It would, of 

 course, in the light of what has been said, be possible to invent any number 

 of alternatives to I. and II. which would lead to perturbations of easily 

 appreciable magnitude, but the important outcome of de Sitter's dis- 

 cussion is that existing astronomical data, place no obstacle in the way of 

 gravitational phenomena being included within the scope of the hypothesis 

 of relativity. The laws given above assume a velocity of propagation for 

 gravitation equal to that of light, such as had for a long time been thought 

 an impossible assumption. 



6 Rend, del circ. mat. dr Pal. xxi., p. 129. 



7 Monthly Notices Roy. Astr. Soc. lxxi. 5. 



